Current mirror techniques are known methods for creating a current source or several current sources that follow a reference current. Current sources can be, for example, light-emitting diode (LED) strings. The basic concept is illustrated in FIG. 1 based on the use of bipolar junction transistors (BJTs). Essentially, the two BJTs are assumed to be matched or identical. Usually, the current in the branch where the collector terminal and the base terminal are tied together forms the reference current. In FIG. 1, the collector current IREF in the BJT Q1 is used as the reference current.
The equations of this circuit are listed as follows:IREF=IC1+2IB  (1)where IC1 is the collector current of BJT Q1 and IB is the base current of both Q1 and Q2. Since IC1=βIB, equation (1) can be expressed as:IREF=βIB+2IB=(β+2)IB  (2)where β is the current gain of the BJT.
For BJT Q2, the collector current is:IOUT=βIB  (3)
From (2) and (3),
                              I          OUT                =                              β                          β              +              2                                ⁢                      I            REF                                              (        4        )            
Since β of a BJT can be in the order of typically 40 to 250, the controlled current source IOUT in (4) is approximately equal to IREF. Therefore, the controlled current source IOUT is said to follow the reference current source IREF.
A current mirror circuit can also be implemented with the use of MOSFETs as shown in FIG. 2. There are other variants of current mirrors such as the Wilson current mirror shown in FIG. 3 and the improved Wilson current mirror shown in FIG. 4. In these existing methods, one branch must be fixed as the reference current source. In the traditional use of the current mirror circuit, this choice of reference current does not change.
It should be noted from existing current mirror techniques that a fixed current source is required as the reference current source. The knowledge of a known reference current source could be a major limitation in some applications such as the dynamic current balancing of LED strings.
FIG. 5 shows one example of such an application in which LED devices are arranged in three strings. Even if each LED string has the same number of series-connected LED devices, the voltage drops across the LED strings are not identical because of slight variations in characteristics of LED devices. There is even a possibility that the current imbalance may change with temperature because LED devices are sensitive to temperature.
Therefore, the imbalance of currents among LED strings is a common problem in LED applications. Such current imbalance would lead to non-uniform light generation among the LED strings. Since the lifetime of LED devices is sensitive to current, if the LED current exceeds the maximum current rating of an LED device due to current imbalance, the lifetime of the LED product would be reduced. In the article titled “Driving high-power LEDs in series-parallel arrays” by Chris Richardson in EDN Magazine, November 2008, on pages 45-49, it was pointed out that even a small voltage difference of 0.42 V between two LED strings can cause a significant current imbalance.
To cope with the current imbalance problem in parallel-connected LED strings, researchers have proposed various methods recently. In the article titled “LED Backlight Driving System for Large-Scale LCD Panels” by Huang-Jen Chiu and Shih-Jen Cheng in the IEEE Transactions on Industrial Electronics, Vol. 54, No. 5, October 2007, on pages 2751-2760, the basic current mirror technique based on an separate reference current source was proposed, as shown in FIG. 6. This approach needs a separate power supply Vd, a resistor Rd and a BJT Qr to form the reference current source. It should be noted that this controlled reference current source is not part of the parallel LED strings, and thus, its formation involves extra costs and increased circuit complexity. This implementation also highlights the fact that existing current mirror techniques require a well-controlled current reference sources, because the current imbalance among the parallel LED strings cannot be predetermined.
Other ideas using the current mirror concept and a separate external power supply (similar to that of FIG. 6) can also be found in the following references:                (1) U.S. Pat. No. 7,605,809 to Wey et al, 20 Oct. 2009, directed to using a power supply and an extra array of comparators for current balancing in a closed-loop control manner;        (2) U.S. Pat. No. 7,642,725 to Cusinato et al, 5 Jan. 2010, directed to using a power supply and a closed-loop control circuit for balancing the LED string currents; and        (3) U.S. Pat. No. 6,621,235 to Chang, 16 Sep. 2003, directed to using a power supply and a closed-loop control circuit for balancing the LED string currents.        
Another previous proposal to reduce current imbalance reported in the article titled “LED Driver With Self-Adaptive Drive Voltage” by Yuequan Hu and Milan M. Jovanovic in IEEE Transactions on Power Electronics, Volume 23, Issue 6, 2008, on pages 3116-3125, uses linear current regulators which are powered by an external power supply Vcc as shown in FIG. 7a. The accurate circuit implementation of FIG. 7a is shown in FIG. 7b. In this approach, the current in each branch has a closed-loop control governed by a central control circuit powered by a separate power supply Vcc, as shown in FIG. 7a. 
Ideas similar to that of FIG. 7a and FIG. 7b were also reported in                (1) “A Balancing Strategy and Implementation of Current Equalizer for High Power LED Backlighting” by Chang-Hua Lin, Tsung-You Hung, Chien-Ming Wang, and Kai-Jun Pai, in International Conference on Power Electronics and Drive Systems PEDS 2007, pages 1613-1617; and        (2) U.S. Pat. No. 7,675,240, 9 Mar. 2010, directed to using the same concept shown in FIG. 7a.         
In summary, the existing current mirror concept for current balancing or sharing applications can be illustrated in FIG. 8, which highlights the requirements of: (i) an external power supply; and (ii) an associated control circuit.
It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative.